Question

A gas pipe line is to be constructed from a storage tank, which is right on a road, to a house which is
600 feet down the road from the tank and 300 feet set back from the road. Pipe laid along the road cost
$8.00/ft while the pipe laid off the road costs $10.00/ft. What is the minimum cost for which this pope
line can be built? Make an objective function with two variables and state the constraints

Answer 1

So, draw the diagram. If the pipeline is in straight segments, and leaves the road x feet from the tank, then the overland distance is
√((600-x)^2 + 300^2)
so the cost of the pipeline is
c(x) = 8x + 10√((600-x)^2 + 300^2)
dc/dx = 8 - 10(600-x)/√((600-x)^2 + 300^2)
dc/dx=0 at x=200, so the minimum cost is c(200) = $6600

Answer 2

how did you get x =200??